The propagation of electromagnetic waves in most materials obeys the right handed rule for the (E,H,β) vector fields, where E is the electrical field, H is the magnetic field, and β is the wave vector. The phase velocity direction is the same as the direction of the signal energy propagation (group velocity) and the refractive index is a positive number. Such materials are “right handed” (RH). Most natural materials are RH materials. Artificial materials can also be RH materials.
A metamaterial (MTM) has an artificial structure. When designed with a structural average unit cell size p much smaller than the wavelength of the electromagnetic energy guided by the metamaterial, the metamaterial can behave like a homogeneous medium to the guided electromagnetic energy. Unlike RH materials, a metamaterial can exhibit a negative refractive index with permittivity ∈ and permeability μ being simultaneously negative, and the phase velocity direction is opposite to the direction of the signal energy propagation where the relative directions of the (E,H,β) vector fields follow the left handed rule. Metamaterials that support only a negative index of refraction with permittivity ∈ and permeability μ being simultaneously negative are pure “left handed” (LH) metamaterials.
Many metamaterials are mixtures of LH metamaterials and RH materials and thus are Composite Left and Right Handed (CRLH) metamaterials. A CRLH metamaterial can behave like a LH metamaterial at low frequencies and a RH material at high frequencies. Designs and properties of various CRLH metamaterials are described in, Caloz and Itoh, “Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications,” John Wiley & Sons (2006). CRLH metamaterials and their applications in antennas are described by Tatsuo Itoh in “Invited paper: Prospects for Metamaterials,” Electronics Letters, Vol. 40, No. 16 (August, 2004).
CRLH metamaterials can be structured and engineered to exhibit electromagnetic properties that are tailored for specific applications and can be used in applications where it may be difficult, impractical or infeasible to use other materials. In addition, CRLH metamaterials may be used to develop new applications and to construct new devices that may not be possible with RH materials.
Various filters based on CRLH metamaterials are examples and are described below.